In this paper we use Darboux’s theory to set up a second order partial differential equation. Later, we will use the variable transformation method to rotate the axis, by 22.8756235 4 degree , in order to remove the interaction terms, which will allow us to find the geodesic equation of two parameter’s extreme value distribution. We also list and prove some useful moments of this distribution. Finally, we apply six transformations that relate this extreme value distribution to other well known distributions, which will extend the value of the results.

In this paper, we present a numerical based approach to develop an analytical solution of an isothermal melt spinning process modeled by a system of coupled non-linear ordinary differential equations. The obtained analytical solution is then compared with the numerical solution.

Aims/ Objectives: To develop a new model called cascade backward propagation neural network performance over a filtered data by clustering algorithm based on robust measure (CFBNFDCARM). The performance of the clustering based neural network approach will be compare with the performances of regression analysis when the data deviate from the assumption of homoscedastic regression.

Methodology: The new developed model was tested using the Airfoil, Aboline and Airline passenger data sets obtained from the UCI machine learning repository in order to compare the performances of regression analysis and a clustering based neural network approach when the data deviate from the assumption of homoscedastic regression. An algorithm based on robust estimates of location and dispersion matrix that helps in preserving the error assumption of the linear regression was introduced in the clustering technique.

Results: The comparison indicated that the results emerging from our developed model gives a better performance when compared with the weighted least square regression as well as the standalone cascade backward propagation neural network for all the data sets considered.

Conclusion: Analysis of the result showed that, the mean square error (MSE) and the root mean squared error (RMSE) in all the cases considered in this study decreases in a definite manner. From the obtained result, it can be seen that, our proposed model (CBPNFDCARM) performed better and can be a better alternative in dealing with heteroscedasticity in data set than both the weighted least square (WLS) and the standalone cascade backward propagation neural network (CBPN).

The process of retrieving relevant documents from user query is to begin with the clustering of documents with high semantic similarities between terms, and lower inner noise values. Here, the research extends normal keywords document clustering techniques in automatic thesaurus construction to building a Concept Based Thesaurus Network. The applied concept matching algorithm uses the Multi-Fuzzy Concept Network to generate sub clustered documents with relative degree of relationship across the clustered document. The proposed system achieved a higher cohesion rate between concepts and lower entropy rate in document. Also, a concise and relevant potential retrieved document were better ranked when compared with other existing document clustering techniques.

In this paper, we introduce a new approach for the Appell polynomials via the sequential representation of the delta operator. Moreover, a theorem which gives the necessary condition for Appell polynomials is proposed. The main objective of this paper is to investigate the characterization of the delta operator for the Bernoulli, the Hermite and the Genocchi polynomials. From our investigation, we are able to prove many interesting propositions for the above mentioned.

Recognition of probe interval graphs has been studied extensively. Recognition algorithms of probe interval graphs can be broken down into two types of problems: partitioned and non-partitioned. A partitioned recognition algorithm includes the probe and nonprobe partition of the vertices as part of the input, where a non-partitioned algorithm does not include the partition. Partitioned probe interval graphs can be recognized in linear-time in the edges, whereas non-partitioned probe interval graphs can be recognized in polynomial-time. Here we present a non-partitioned recognition algorithm for 2-trees, an extension of trees, that are probe interval graphs. We show that this algorithm runs in O (m) time, where m is the number of edges of a 2-tree. Currently there is no algorithm that performs as well for this problem.

The aim of this work is to study the 2-D boundary layer stagnation point flow from a stretching surface embedded in a porous medium with velocity/thermal slip conditions on the wall and heat generation or absorption. Under boundary layer approximations, the governing boundary layer equations of the problem can be reduced to two ordinary differential equations and solved by using Maple code for some values of the problem parameters. The influences of problem parameters on the flow characteristics such as velocity and temperature profiles, skin friction and the Nusselt number are clearly discussed graphically and in tables. It is found that the flow field is influenced greatly by the ratio of the free stream velocity (u_{e}) and the stretching velocity (u_{w}) as well as the velocity/thermal slip parameter. We have compared our results with open literature and found excellence agreement.